Circuit board microwave filters

ABSTRACT

A microwave filter has resonator comprised of a cylindrical structure having conductive walls filled with a dielectric material where the cylindrical structure is recessed inside a multi-layered substrate. First and second conductive coupling arms are disposed on a top layer of the substrate for coupling signals to the cylindrical structure. The conductive coupling arms are separated by a dielectric layer. The first and second conductive coupling arms extend away from the center of the cylindrical structure to form a microstrip line. The cylindrical structure further comprises a bottom portion having a solid conductive bottom plate perpendicular to the axis of the cylinder and a bottom conductive ground layer separated from the conductive bottom plate by a second dielectric layer.

RELATED APPLICATION

[0001] This application claims priority from a previously filed UnitedStates provisional application entitled CIRCUIT BOARD MICROWAVE FILTERSfiled on Nov. 2, 2002, application Ser. No. 60/338,087 and isincorporated herein by reference.

FIELD OF THE INVENTION

[0002] This invention relates to an Radio Frequency spectrum structureand more specifically to circuit boards/substratemicrowave filteremploys a resonator structure

BACKGROUND OF THE INVENTION

[0003] Microwave and RF filters are common components of communicationdevices. Both transmitters and receivers use filters for rejection ofsignals in the unwanted frequency bands. A major application of suchfilters is in the cellular/PCS phones. The most commonly used filter forcellular/PCS application is the coaxial ceramic type in which severalcoaxial ceramic resonators with very high relative dielectric constantsare coupled to each other. These filters often are installed on top ofcircuit board and substantially increase height to the board thickness.As a result the filters are one of the components that restrict theimplementation of a thin cell/PCS phones. Multi-layer circuit board withseveral layers of dielectric material and plated through blind via holeshave become a common technology used in the cellular telephone handsets.

[0004] With the advent of Monolithic Microwave/millimeter waveIntegrated Circuits (MMIC, MmmwIC) the needs for implementing highperformance/space efficient filters have been increasing. Thesemiconductor substrate real estate especially material suitable formicrowave/millimeter wave applications (e.g., GaAs) is costly andrestrictive. Filters are often implemented off the chip. There is agreat demand for means providing size reduction leading to costefficient on chip implementation of filters.

SUMMARY OF THE INVENTION

[0005] A new RF/Microwave filter using a novel resonator is introduced.The resonator is composed of a plated through hole implemented(cylindrical with circular or any arbitrary cross section) similar to avia hole and extra onboard metalization implemented in various possiblelayers of a circuit board or any form of substrate.

[0006] The conductive cylinder is separated by a dielectric layer on topand on the bottom when necessary. Inside the cylinder is filled up withdielectric material or hollow. Almost any type of transmission linewhich can be implemented on a circuit board or a substrate can beutilized.

[0007] Various type of transmission lines such as described in can beemployed signals carried by these transmission lines are coupled to thenovel resonator of the present invention.

[0008] In addition a new type of microstrip line called compositemicrostrip line can be utilized which is suitable for certain types ofimplementation. In the integrated circuit technology where the height ofdielectric layers are limited the alternative transmission line typessuch as slot lines are often implemented.

[0009] In accordance with other embodiment of the invention theresonator circuit is employed to function as part of a resonator forother microwave components such as oscillators, power dividers, andbaluns.

[0010] This invention provides the means to build RF/microwave/mm wavecomponents including filter using a novel resonator on a multi-layerboard or on substrate in order to avoid external filters and theirassociated cost and size by means of using composite microstrip lines,combination of simple microstrip lines, or other types of thetransmission lines.

[0011] Depending on dimensions and the relevant frequencies, platedthrough holes could be considered as lumped inductive elements,evanescent mode waveguide or propagating waveguide. In all the threementioned cases the plated through holes provide inductive reactanceneeded for resonance condition.

[0012] Band pass filters are the most common type of filters used incommunications. Usually in order to obtain rejection outside of the passband of the filter, multi-section filters are required. Each section isa resonator which an LC equivalent circuit is obtainable. In thisinvention the cylindrical structure mainly provides the inductiveportion of the resonance and the capacitive components are constructedvia the any two conductors separated via dielectrics or hollow spacebetween them.

BRIEF DESCRIPTION OF DRAWINGS

[0013] FIGS. 1-a through 1-j illustrate various exemplary standardtransmission lines that are usable in this invention and to coupleenergy to a resonator structure in accordance with various embodiment ofthe present invention taken from.

[0014] FIGS. 2-a and 2-e depict multi layered board/substrate usable forvarious embodiment of this invention.

[0015]FIG. 3 is depicts a three dimensional view of a bandpass resonator

[0016]FIG. 4 depicts various exemplary cross sectional view ofcylindrical structures usable for various embodiment of this invention.

[0017]FIG. 5 through are frnt view, side view and top view of exemplaryresonator.

DETAILED DESCRIPTION OF THE DRAWINGS

[0018] FIGS. 1-a through FIG. 1-j depict the cross section of a varietyof types of transmission lines taken from the reference K. C. Gupta,Ramesh Garg, I. J. Bahl, “MICROSTRIP LINES and SLOT LINES”, Copyright ©1979 by Artech House, Inc., pages 1-3, the entirety of which isincorporated herein reference. FIGS. 1-a through 1-j illustrate variousexemplary standard transmission lines that are usable in this inventionand to couple energy to a resonator structure in accordance with variousembodiment of the present invention taken from.

[0019]FIG. 1-a depicts the cross section of a microstrip line.

[0020]FIG. 1-b depicts the cross section of a slotstrip line.

[0021]FIG. 1-c depicts the cross section of a coplanar waveguide.

[0022]FIG. 1-d depicts the cross section of a coplanar strips.

[0023]FIG. 1-e depicts the cross section of an inverted microstrip line.

[0024]FIG. 1-f depicts the cross section of a suspended microstrip line.

[0025]FIG. 1-g depicts the cross section of a microstrip line withoverlay.

[0026]FIG. 1-h depicts the cross section of a strip dielectric waveguide.

[0027]FIG. 1-i depicts the cross section of an inverted strip dielectricwave guide.

[0028]FIG. 1-j depicts the cross section of an inverted stripline.

[0029] FIGS. 2-a through 2-e depict multi layered board/substrate usablefor various embodiment of this invention.

[0030] FIGS. 2-a illustrates a multi-layered substrate 201, is composedof three-layers of dielectric located between a ground plane underneathand a narrow conductive strip above forms a “three-layered compositemicrostrip line”.

[0031] FIGS. 2-b illustrates a multi-layered substrate 202, is composedof two layers of dielectric located between a ground plane underneathand a narrow conductive strip above forms a “two-layered compositemicrostrip line”.

[0032] FIGS. 2-c illustrates a multi-layered substrate 203, is composedof three-layers of dielectric and three conductive layers, wherein aground plane is on the bottom and a narrow conductive strip on top and alayer of dielectric separates the top and the intermediate conductivelayer referred to as the “intermediate ground plane”.

[0033] FIGS. 2-d illustrates a multi-layered substrate 203, is composedof three-layers of dielectric and four conductive layers, wherein theconductive layres and dielectric layers are alternatively located and asa result simple microstrip lines could be formed by any two consequetiveconductors.

[0034]FIG. 3 is depicts a three dimensional view of an exemplaryembodiment of the invention, a bandpass resonator using 203 type ofmulti-layered substrate, a cylindrical structure with a circular crosssection located vertically.

[0035]FIG. 4-a through 4F depict various exemplary cross sectional viewof cylindrical structures usable for various embodiment of thisinvention.

[0036]FIG. 4-a depicts a circular cross section.

[0037]FIG. 4-b depicts an eliptical cross section.

[0038]FIG. 4-c depicts a rectangular cross section.

[0039]FIG. 4-d depicts a rectangular cross section with round cornerswhich is easy to manufature in the printed circuit board technology.

[0040]FIG. 4-e depicts a double-circular cross section.

[0041]FIG. 4-f depicts a quadruple ridged cross section.

[0042]FIG. 4-g depicts a double ridged cross section.

[0043]FIG. 4-h depicts a highly capacitive double ridged cross section.

[0044]FIG. 4-h depicts a highly capacitive quadruple ridged crosssection.

[0045] FIGS. 5-a and 5 b illustrate a resonator structure 100 inaccordance with one embodiment of the invention.

[0046] The resonator is composed of a cylindrical structure 98 withconductive walls 101, which is filled up with dielectric material or airor hollow 103 although the invention is not limited in the scope in thatrespect. For example as will be discussed in more detail latercylindrical structure 98 can be filled up with a conductor material.

[0047] Cylindircal structure 98 is recessed inside a multi-layeredsubstrate. FIG. 3a-3 e illustrate various multi-layered substrates suchas 201, 202, 203, 204, 205. A multi-layered substrate is an arrangementthat contains

[0048] The cylindrical structure has an arbitrary type of cross sectionsuch as those illustrated in FIG. 4. The axis 104 of the cylindricalstructure is perpendicular to the layers of the substrate. The top layercontains two conductive coupling arms 105, 106 which are utilized forcoupling of signal into and from the cylindrical structure. The couplingarms 105 and 106 are both located above the cylindrical structure aresituated very close to the top of the cylindrical structure and aresymmetrical with respect to the axis of the cylinder and are separatedby a dielectric layer.

[0049] The cylindrical structure 98 extends down into the substrate 108and at its lowest portion has a solid conductive bottom plate 109perpendicular to the axis of cylinder.

[0050] The conductive bottom plate 109 is separated from a bottomconductive ground layer 111 by another dielectric layer 110 or is partof the bottom conductive ground layer of 111. Each conductive couplingarm 105/106 are located on the opposite sides with respect to the axisof cylinder and are extending away from the center of the structure intothe space above the substrate forming a microstrip 96 such as the oneillustrated in FIG. 11 or a composite microstrip structure 94 such asthe one illustrated in FIG. 5a in conjunction with dielectric layers107, 108 and 110 of the a multi-layer substrate.

[0051] Partly, or entirely the extensions 112 and 113 of microstripstructure 96 or composite microstrip structure 94 above dielectriclayers 107, 108 and 110 constitute other reactive elements such as shuntor series reactive elements or their combination in order to provide therequired resonance condition at the appropriate impedance level andcoupling to the next resonator or input/output port of the filter orRF/microwave/mm wave component. Examples of reactive elements are shuntcapacitors, formed by widening microstrip line/composite microstripline, series capacitors formed by overlay capacitor, inter-digitalcapacitor, microstrip/composite microstripline gap, or an externalcomponents attached, etc, and series inductor formed by a narrowmicrostrip line/composite microstrip line with straight or curved orzigzaged or shunt inductor formed by one or a combination of shortedmicrostrip line(s)/composite microstrip line(s) with straight or curvedor zigzaged.

[0052]FIG. 5-a and FIG. 5-b depict two cross sectional view of apossible embodiment of the invention wherein the composite microstripline is composed of three layers and the bottom plate 109 is separatedfrom the bottom ground layer 111 by a dielectric layer 110.

[0053]FIG. 6 depicts a cross sectional view of a possible embodiment ofthe invention in which the bottom plate 109 is part of the bottom groundlayer 111.

[0054]FIG. 7 depicts a possible top view of a resonator of FIGS. 5 and 6where a series capacitor is implemented by introduction of a gap in themicrostrip lines on each side of the resonator.

[0055]FIG. 8 depicts a portion of a possible top view of the resonatorsof FIGS. 5 and 6 where shunt capacitors are implemented by introducininga wide microstrip line(s) and on each side of the resonator.

[0056]FIG. 9 depicts a cross sectional view of a possible embodiment ofthe invented resonator in which an addition conductive ground layer 114is underneath the dielectric layer 107. As a result the conductors inthe top layer i.e., the continuation of the coupling arms 112 and 113outside of the areas above the cylindrical structure 98 and thisadditional ground layer 114, form a microstrip line structure. The useof this type of microstrip line structure is to keep the signal energyabove the cylindrical structure above the conductive cylindrical wall,in order to eliminate reflection by cylinder wall which could occur inthe composite microstrip type of substrate.

[0057]FIGS. 9, 10, 11, 12, 13, 14, 15 depict addition of a conductiveannular ring 115 to the top edge of the conductive cylindrical wall 101in order to obtain more capacitance between the coupling arms 105,106and the cylinder 101.

[0058]FIG. 11 depicts another embodiment of the invention in which theannular ring 115 is utilized and the cylinder bottom plate 109 isseparated from the bottom ground layer 111 by the dielectric layer 110and also, an addition conductive ground layer 114 underneath thedielectric layer 107 for reduced reflection from the conductive cylinderwall 101.

[0059]FIG. 10 depicts a possible top view for FIGS. 9 and 11.

[0060]FIGS. 12 and 13 depict an embodiment of the invention with strongcoupling from wide conductive coupling arm 105/106 and their extensionoutside of the area above the cylinder.

[0061]FIGS. 14,15 and 16 depict an embodiment of the invention withstrong coupling from wide conductive coupling arm 105/106 and theirextension outside of the area above the cylinder. FIG. 14 and 16 bothhave a conductive top in order to obtain more capacitance between thecoupling arms and the cylindrical wall.

[0062]FIGS. 18,19 are possible top views for FIG. 17. FIG. 18 depicts acircular cross section for the conductive cylindrical wall 101. FIG. 19and 20 depict a rectangular cross section for the conductive cylindricalwall 101. FIG. 19 depicts rectangular conductive coupling arm 105/106separated by a simple gap located at the center of the cylindricalstructure and perpendicular the direction of the axes of the conductivecoupling arm 105/106.

[0063]FIG. 21 depicts rectangular conductive coupling arm 105/106 arestrongly coupled to each other by use of an inter-digital capacitor.

[0064]FIG. 21 and 22 depict conductive coupling arms 105/106 have aslanted (diagonal) gap.

[0065]FIG. 23 depicts conductive coupling arms 105/106, which arecoupling energy to the cylindrical structure by loop coupling.

[0066]FIG. 24 and 25 depict each of the conductive coupling arms105/106, which are spiral and rotates around the other in order toobtain strong coupling

[0067] In another embodiment of the invention, a transmission resonator92 (as opposed to reflection type discussed up to this point) whereinthe resonator incorporates a transmission type of cylindrical structure98 recessed in a multi layered 205 substrate which the conductivecylinder wall 101 is open at both ends and there is no bottom conductingplate for reflection of signals. The substrate is composed of threedielectric layers 107,108,110 and four conductive layers. The topconductive layer contains the conductive coupling arm 105 its extension112 and ground plane 131. The top intermediate conductive 130 isseparated from the top conductive containing the conductive coupling arm105 its extension 112 and ground plane 131 ground by a dielectric layer107. Similarly, the bottom conductive layer contains the conductivecoupling arm 106 its extension 113 and ground plane 111. The bottomintermediate conductive 132 is separated from the top conductivecontaining the conductive coupling arm 105 its extension 112 and groundplane 131 ground by a dielectric layer 110. The middle dielectric layer108 is between the two intermediate ground layers 132 and 130 andcontain the conductive cylinder wall 101. Depending on the type ofcoupling of resonator coupling the extensions 112 and 113, theintermediate ground layers 130 and 132 possibly connected to theconductive cylinder wall 101. Therefore the space 129 located betweenthe intermediate ground plane 130 and the conductive cylinder wall 101or space space 128 located between the intermediate ground plane 132 andthe conductive cylinder wall 101 in certain implementations could beconductive.

[0068] Examples of the transmission resonator are depicted in FIGS. 26,27, 28, 29, 30, 31, 32, 33, 34.

[0069]FIG. 26, 27 depict a transmission resonator in which a spiralconductive coupling arm 105 coupled to a transmission resonator 92. Thesignal is coupled to the coupling arm via an interdigital capacitor 112from a microstrip line located on the top layer. The signal is coupledout of from the bottom side of cylindrical structure 98 a spiral arm 106throuhgh the inter-digital capacitor 113 to the out put microstrip line.

[0070]FIG. 28, 29 depict a transmission resonator in which a straightconductive coupling arm 105 coupled to a transmission resonator 92. Thesignal is coupled out of from the bottom side of cylindrical structure98 a via a stright conductive arm 106 out of the strcucture. throuhghthe inter-digital capacitor 113 to the out put microstrip line.

[0071]FIG. 30 depict a transmission resonator in which a straightconductive coupling arm 105 coupled to a transmission resonator 92. Thesignal is coupled to the coupling arm via an microstrip gap capacitor112 from a microstrip line located on the top layer. The signal iscoupled out of from the bottom side of cylindrical structure 98 astraight arm 106 through the microstrip gap capacitor 113 to the out putmicrostrip line.

[0072]FIG. 31, 32 depict a transmission resonator in which a loopconductive coupling arm 105 coupled to a transmission resonator 92. Thesignal is coupled out from the bottom side of cylindrical structure 98 avia a loop conductive arm 106 out of the structure through theinter-digital capacitor 113 to the out put microstrip line.

[0073]FIG. 33, 34 depict signal coupled from a stripline via aninter-digital capacitor to a shielded reflection resonator structure(with a rectangular cross section) coupled via a straight conductivecoupling arm 105 coupled a transmission resonator 90. The signal iscoupled out of from the opposite side of cylindrical structure 98 via astraight conductive arm 106 out of the structure via anotherinter-digital capacitor 113 to the out put port strip line.

[0074]FIG. 35, 36 depict signal coupled from a micro to ridgedcylindrical structure 98 a via a straight conductive arms 106/105. thearms are located on top of the ridges in order to maximize the coupling.

[0075]FIG. 37, 38 depict signal coupled from a micro to ridgedcylindrical structure 98 a via a straight conductive arms 106/105. thearms are attached to the ridges by conductive pins.

[0076]FIG. 39 depicts an embodiment of the invention using a slot linesas were describe in FIG. 1-b. Siot lines are commonly used in MMIC's aswell as the other types of transmission lines describe in FIGS. 1-through 1-j. Similarly, all types of the abovementioned transmissionlines are usable to couple in conjunction with the cylindrical structure98.resonator. re abovementioned.

[0077]FIG. 40 depict implementation of filter using the inventionreflection type of the invention resonator

[0078]FIG. 41 depict implementation of filter using the inventiontransmission type of the invention resonator

[0079] For the purpose of illustration the operation of the resonantstructure is described hereinafter

[0080] Resonators serve as the basic components for many types offilters. In general they are composed of various inductive andcapacitive elements. The capacitive elements are constituted by any twoconductors separated by dielectric material or hollow space in betweenor portions of waveguides or transmission lines. Inductive elements areconstituted by conductors, waveguides, and portions of transmissionlines. However in distributed elements, a capacitive element at certainfrequency can behave as an inductive element at another frequency andvice versa. Lumped elements are small in comparison to the wavelengthand their behavior from inductive to capacitive behavior does not alterfrom frequency change.

[0081] Depending on dimensions and the relevant frequencies platedthrough holes could be considered as lumped inductive elements,evanescent mode waveguide or propagating waveguide. In all the threementioned cases the plated through holes provide inductive reactanceneeded for resonance condition. Band pass filters are the most commontype of filters used in communications. Usually in order to obtainrejection outside of the pass band of the filter, multi-section filtersare required. Each section is a resonator which an LC equivalent circuitis obtainable. In this invention the cylindrical structure mainlyprovides the inductive portion of the resonance and the capacitivecomponents are constructed via the any two conductors separated viadielectrics or hollow space between them.

[0082]FIG. 51 depict a resonator with the electric field linestravelling towards the resonator and partially reflecting from the wallsof the cylinder. The reflection from conductor is resulted from applyingthe boundary conditions at the cylinder conductive wall. Since the totaltangential component of electric field vanishes on a conductive surface,an opposite electric travelling in the reverse direction, i.e., awayfrom the cylinder must exist to satisfy the boundary conditions. In FIG.51, the solid lines 80 represent the vertical component of electricfield travelling towards the cylinder wall and the dashed lines 81represent the electric field travelling away the cylinder wall. Andlines 82 are coupled to the resonator. As noticeable in the figure theenergy of reflected wave field travelling in dielectric layer designatedwith a dielectric constant of ∈₁ could be significant portion. However,in dielectric layer designated with a dielectric constant of ∈₃ theconductive wall is not present and such reflections as severe of layer∈₃ does not occur and a good portion of the energy of the wave iscoupled to the cylinder.

[0083] However, as the reflected wave in layer ∈₁ travels back theboundary conditions between the two dielectric layers ∈₁ and ∈₃, i.e.,continuity of normal component of displacement vector D, i.e,D_(1n)=D_(3n) predicts the presence of reflected wave in the ∈₃ layerdue to reflections in layer ∈₁ constituting a reflected voltage V⁻travelling away from the cylinder. At any arbitrary point on thetransmission line 83 the ratio of Γ=V⁻/V⁺ corresponds to an presence ofequivalent reactive element (inductive or capacitive) present at theboundary of the cylinder.

[0084] In order to decrease the reflection losses as a result of theabove-mentioned phenomena, one of the following techniques could beutilized.

[0085] a. Introduction of a matching elements that cancels the effect ofthe above mentioned reactance, i.e., introducing of another reactiveelement with a conjugate match which would further reduce the bandwidthof the resonator which might not be desirable in most situations inaddition to requiring more space.

[0086] b. A rough analysis of energy inside various layers of acomposite microstrip line substrate indicates that the dielectric layerswith higher dielectric constant carry higher energy density. Thisanalysis does not include the spread of the fringing field and othersecondary effect but it provides a guideline for selection of dielectriclayers for minimizing the energy of reflected signals by the metallicwall of the structure. The energy density inside a dielectric materialis proportional to ∈.|E|² the energy of the portion of the wavetravelling inside ∈₁ layer can be minimized by selecting a significantlyhigher dielectric constant for ∈₃ and than ∈₁ (∈₃>>∈₁). Since theboundary conditions predict that normal component to the boundary ofelectric flux density D is continuous at the boundary (in the absence ofelectric charges at the boundary)

D_(1n)=D_(3n)

∈₁ .E ₁=∈₃ .E ₃

E ₃ /E ₁=∈₁/∈₃<<1

[0087] or:

E _(3n) <<E _(1n)

[0088] Therefore, without consideration of secondary effects such as thenon-uniform and fringing fields in the two dielectric layers, thisanalysis indicates that if the selection of the dielectric constants ∈₁and ∈₃ is in such a way that the energy in layer ∈₃ is higher than ∈₃:

∈₁ .h ₁ .w.|E ₁|²<<∈₃ .h ₃ .w.|E ₃|²

[0089] to a good extend even h₁>h₃ the reflection of the wave by thecylindrical wall would not be of concern. This method has itslimitations. The manufacturing process of such a high dielectricmaterial (e.g., ∈₃>30) and adding to a regular circuit board is costly.Similarly, in the case of implementation of the resonator insemiconductor integrated circuits such high dielectric constantssubstrates are not sensible.

[0090] c. By utilizing an intermediate conductive layer a micro stripline is established between this intermediate layer and the topconductor in the layer designated as layer ∈₃. Thereby, the energy ismainly present in the layer ∈₃ and the presence of energy in thedielectric layer designated as ∈₁ is eliminated and as a result theproblems associated with the reflections from the cylinders conductivewall is nonexistent. FIG. 52 depicts this configuration. A simplemicro-strip transmission line is established between the top conductorand an intermediate conductor layer which serves as the ground asdepicted in the cross sectional cuts of FIG. 52. In this method theproblem arising from the reflections resulting from the electric fieldbeing shorted by the conductive boundary of the resonator is eliminated.Also, there is no need for other reactive matching elements forproviding the canceling effects for the reflected waves. Therefore,wider bandwidth can be obtained from each resonator. Furthermore, sincethe layer ∈₃ has shorter height the width for capacitive elements arenarrower than the case where the capacitive elements were established bythe combination of both layers ∈₁ and ∈₃. As a result, the expense ofhigh dielectric constant material is avoided and any ordinary circuitboard material can be used for layer ∈₃. In addition, size reduction isachieved in this type implementation, i.e., the required real estatereduced as the required capacitance can be obtaind from using a smallerarea due to height reduction. Since h is significantly smaller in FIG.%%12 than FIG. 11, the capacitance area A is reduced by the accordinglyin order to obtain the same capacitance C=∈A/h. if similar dielectricmaterial is used.

[0091] d. In a variation of the invention as in FIG. 53, to overcomeproblems resulting from resulting from very thin dielectric layer heighth₃. When the height of the dielectric layer h₃ is very small in somemanufacturing processes tolerances of height becomes excessive and theresultant capacitors mad using that layer are inconsistent. In addition,when the height h₃ the characteristic impedance of transmission lineswith practical line widths tend to be very low and the range of requiredthe characteristic impedances are often not be attainable. FIG. 153utilizes a dielectric layer ∈₄ with a moderate height h₄. The height h₄of this layer is not as high as layers h₁+h₃ which causes significantreflection problems

[0092] In relation to dimensions of the resonators, versus the operatingfrequency, there are three different modes of operations: lumped,evanescent, propagating mode of operation also a combination of themi.e., the dimension in one direction is small in comparison to a quarterwavelength but not small in another direction. The lumped element typeprovides the most space efficient resonator wherever appropriate.

[0093] 1. Lumped. Resonators

[0094] For frequency ranges which the dimensions of the structure aremuch smaller than a quarter wavelength, lumped element equivalentcapacitances and inductances are the simplest and appropriate.

[0095]FIG. 54-a depicts the longitudinal cross section of a possibleimplementation of such resonator. The equivalent components are drawn onthe figure and the consequential equivalent circuits are depicted inFIG. 100b.

[0096] The values for C₁ can be calculated with a good approximationwith electrostatic analysis using equations provided for calculation ofcapacitance of gaps in micro-strip lines which is by provided referencescited below these equations do not contain the effects of the wall ofthe cylinder but values are provide a sufficiently close for firstdegree approximation of C1:

[0097] Ba=−2*h*log(cosh(pi*s/2/h))/lambda

[0098] Bb=h*log(coth(pi*s/2/h))/lambda

[0099] BA=(1+Ba*cot(beta*s/2))/(cot(beta*s/2)−Ba)

[0100]C1=((1+(2*Bb+Ba)*cot(beta*s/2))/(cot(beta*s/2)−2*Bb−Ba)−BA)/(2*pi*f*Z0)

[0101] Reference is made here to Handbook of Microwave and opticalComponents, Volume 1, Edited by Kai Chang, 1989, the entirety of whichis incorporated herein by reference. Reference is also made to ComputerAided Design of Microwave circuits, K. C. Gupta, Ramesh Garg, RakeshChadha, 1981, the entirety of which is incorporated herein by reference.Reference is also made to Minoru Maeda, “An Analysis of Gap inMicrostrip Transmission Lines”, IEEETRANSACTIONS ON MICROWAVE THEORY ANDTECHNIQUES., VOL. MTT 20, NO.26 June 1972, the entirety of which isincorporated herein by reference.

[0102] For calculation of C₂ and C₃ the following methodology can be isutilized. First the capacitance of a cylindrical structure with bottomside walls are attached together at zero potential and the top surfaceis at a different potential is calculated. FIG. %% 101 depicts acylindrical structure with bottom side and side walls are attachedtogether at zero potential. The top surface is at potential V0. Thecapacitance C which is the total capacitance between the top surfacesinside of the rest of the structure can be calculated by solvingPossion's equation ∇²V=0 for a conductive cylinder as of FIG. 102obtaining a series solution for V: $\begin{matrix}{{V\left( {r,z} \right)} = {\sum\limits_{n = {odd}}{4*{{V0}.}*{{\sinh \left( {n*{pi}*{z/d}} \right)}.}*}}} \\{{{{\sin \left( {{n*{pi}*{r/d}} + {n*{{pi}/2}}} \right)}.}/\left( {n*{{pi}.}*{\sinh \left( {n*{pi}*{h/d}} \right)}} \right)}}\end{matrix}$

[0103] Such analysis leads to calculation of the potential distributionin the space inside and on the surfaces of the cylinder. By obtainingE=−∇V in the radial direction at the side walls and the normal componentof the electric field to the walls is obtained. Similarly, by applyingE=−∇V in the z-direction at the top and bottom surfaces the normalcomponent of the electric field to the walls is obtained. Charge densityon these surfaces can be calculated by:

ρ_(s) =|D _(n)|=∈₀.∈_(r) .|E _(n)|

[0104] The total electric charge Q located inside the surface above thecylinder located on the top plate is calculated numerically by takingsurface integral over the top plate. The static capacitance is obtainedfrom C_(layer-2)=V₀/Q which is the capacitance of the capacitor formedby the circular area of the top plate and the walls and the bottom plateof the structure. If the top plate is extended outside of the cylinder asimilar concept is used to obtain the capacitance between the side wallarea of the cylinder and the surfaces of the top plate located outsidecylinder. If the dielectric constants are the same, i.e., ∈₂=∈₁, thecapacitance for the outside area of the plate would approximately be thesame as the capacitance for the inside surface, i.e.,C_(layer-1)≅C_(layer-2). this is due to the fact that the chargedistributions on the top plate is mostly concentrated above in the areabove the cylinder side wall. However since in general ∈₃≠∈₁, thecapacitance for the outside capacitance is obtained by applying theratio of the dielectric constants as the correction factor i.e.,C_(layer-1)≅(∈₁/∈₂). C_(layer-2) and C_(Total)=C_(layer-1)+C_(layer-2).

[0105] In FIG. 57-b the center of the charge distribution on the sidewall is marked as h_(cap-eff) which is obtained by finding the center ofthe charge on the side wall or more accurately by integrating the overthe inverse distance multiplied by the charge distribution on thecylinder wall and finding the inverse. FIG. 58 depicts a cylinder with acircle drawn on the cylinder wall corresponding to the center of thecharge. This ring represents the effective location of the impressedsignal by the top plates on the side wall.

[0106] The equivalent area of this capacitor is given by:

A _(eff-i) =C _(layer-i) .h _(eff-cap-i)/(∈₁.∈₁₀)

[0107] which corresponds to the area of an annular plate under therelevant portion of the top plate separated by a distance of distance ofh_(eff-cap-i) from the top plate for i=1, 2. The following formulationis valid for very small h₃, the height of thin thickness of dielectriclayer ∈₃. To calculate the effects of dielectric layer ∈₂ on thecapacitance is performed by including the effects of a series capacitorwith area of A_(eff) and height of the layer, h₃:

[0108] Where:

C _(layer-3-i)=∈₃ A _(eff-i) /h ₃

[0109] Therefore:

C _(total) =C _(layer-3-1) +C _(layer-3-2)

[0110] C_(total) represents the value capacitance of a solid plateseparated covering above the structure. However, for the bandpass casewhen there is a gap in the top plate, the capacitances C₂ and C₃ whichcorrespond to the capacitance between each arm and the cylinder asdescribed in are calculated by calculating the fraction of C_(total)proportional to the area which each arms covers. When the arms arecovering the area above the cylinder and the gap is small:

C ₂ =C ₃ ≅C _(total)/2

[0111] The equation for inductance of via hole is given in the referenceModeling via hole grounds in microstrip Golfarb, M. E.; Pucel, R. A.IEEE Microwave and Guided Wave Letters [see also IEEE Microwave andWireless Components Letters], Volume: 1 Issue: 6, Jun. 1991, Page(s):135-137, the entirety of which is incorporated herein by reference:

L=u 0*(h*(ln((h+sqrt(a{circumflex over ( )} ² +h{circumflex over ( )}²)/a))+1.5*(a+sqrt(a{circumflex over ( )}2+h{circumflex over( )}2))))/2/pi

[0112] This equation is corrected empirically from the previousderivations. It is stated in the Goldfarb reference that the aboveequation follows very closely to greater extent with the actualmeasurements as well as electromagnetic simulations than the equationsprovided by earlier works. In the case of the structure under discussionin this invention, when the effective height h_(eff-ind) instead of theactual height h is used is in the above equation a more accurateassessment of the inductance of the cylinder is expected.

[0113]FIG. 55 depicts a variation of the resonator structure. An annularring is added to the top end of cylindrical wall in order to increasethe interaction between the cylinder and the coupling arms. Addition ofthis ring increases the capacitances C₂ and C₃ and more coupling to theresonator is obtained. As a result of adding the annular ring thelocation of the hypothetical ring corresponding to the center of thecharge as of FIG. 54 is moved up closer to the coupling arms and theeffective height of the cylinder h_(eff) is increased. If the ratio ofthe width to the height of this capacitor is large the effect offringing fields can be neglected and the capacitance between the armsand the cylinder can be simply calculated from simple capacitorequation: C=∈₃.∈₀.A/h₃, where A is the area of the portion of thecoupling arm located above the annular ring.

[0114] Similarly in order to obtain more capacitance between thecylinder bottom plate and the ground, the metalization in the bottom canbe extended as in FIG. 56

[0115] Often, the need to size reduction or in effect lowering thefrequency requires larger capacitors for the gap capacitance, i.e. thecapacitance between the arms C₁. This can be accomplished byimplementing an inter-digital capacitor or a slanted cut. The equationsfor calculation of capacitance for interdigital and overly capacitor isprovided in various texts, e.g., the reference K. C. Gupta, Ramesh Garg,Rakesh Chadha, “COMPUTER AIDED DESIGN OF MICROWAVE CIRCUITS”, “1981,pages 213-219, the entirety of which is incorporated herein byreference. FIGS. 25 depicts coupling via two spiral conductors“inter-spiral coupling” which offers more coupling between the two armsand therefore a higher value for C₁.

[0116] Accuracy

[0117] A more accurate calculation for the component values or anyportion or the entire structure can be deviced by using commerciallyavailable electromagnetic analysis software packages such as SONNET,HFSS or similar packages available for three-dimensional structures.

[0118] Filter Design Procedure

[0119] There are various approaches to for a filter or otherRF/microwave circuit component design using the resonators discussed inthis invention. The major important parameters for filter synthesis isimportant parameters is bandwidth and center frequency at certainimpedance level in simple resonators. Reference cited below providedesign procedures based on lumped element equivalent resonator circuitswhich is common practice to those skilled in the art. Reference is madeherein to Reference Data for Engineers: Radio, Electronics, Computer,and Communicatios, seventh edition, Edward C. Jordan, Editor in chief1986, the entirety of which is incorporated herein by reference. Seealso the Chang reference. Reference is also made to Arthur B. Williams,Fred J. Taylor, “Electronic Filter Design Handbook: LC, Active andDigital Filters”, Second Edition, 1988,

[0120] 1) For each resonator needed in a filter has a known componentvalues or set of S-parameters in the band of interest. The two portS-parameters of the desired resonator can be obtained from the lumpedelement synthesized circuit by using any circuit simulator program.Also, the two port S-parameters of the desired resonator can be obtainedusing an electromagnetic analysis software packages. Using optimizationtechniques an equivalent LCR similar to the topologies given in FIGS.%%% which closely follows two port S-parameters obtained fromelectromagnetic program or actual measurements in the band of interestcan obtained. An equivalent circuit with estimated values is used to acircuit simulation program and an optimizer (e.g., Microwave Office,Super Compact, Touchstone) optimizes the circuit component values in theequivalent until a close match of S-parameters in the band of interestis obtained. The two important parameters in a simple resonator isbandwidth and center frequency at the impedance level of interest. Oftenthe practical resonators provide the bandwidth and center frequency at adifferent impedance level. Physical dimensions are changed e.g., widthof annular disc for changing C2 and C3 or change of the gap type or sizefor changing C1 until the center frequency and the bandwidth of theresonator are obtained. Filter impedance is adjusted to the properimpedance (often 50 Ohms) by introducing a combination of shunt andseries reactances at the input and output or any type of impedanceinverter the required level is obtained which is trivial for theengineers skilled in the art.

[0121] 2) In a process of trial and error a family of curves can beobtained for center frequency and bandwidth for different dimensions,using standard thickness and standard relative dielectric constants ofdifferent layer. Equivalent circuits can be obtained from the predictedbandwidth and center frequencies. In order to obtain a resonatoroperating at a lower frequency metalization can be added to as the shuntcapacitances to the resonator. Alternatively, the family of the curvescan be plotted for the relationship between the physical dimensions anddielectric constant versus the elements of equivalent circuits. Theequivalent circuit concept serves as a preliminary synthesis tool.

[0122] Using standard techniques for synthesis of lumped element LCcircuit provided in the references cited below. In order to realizeactual design from the lumped element LC network and using the family ofthe curves to obtain the physical dimensions for the desired filter. Seethe Chang reference. See the Williams reference.

[0123] 2. Evanescent. Mode Resonance

[0124] In guide structures, evanescent mode of operation corresponds tooperation below the cutoff frequency of the guide. The advantage isreduction of the size but filled with dielectric material even providesfurther size reduction:

[0125]FIGS. 3,5 through 39. depict a resonator based on evanescent modeof operation.

β=2π/λ=2π(μ∈)^(1/2) f

[0126] λ is wavelength in infinite media,

β_(mn) =β.{square root}{square root over (1−[(f _(c))_(eff) /f]²)}

(f _(c))_(mn)={square root}{square root over((m.π/a)²+(n.π/b)²)}/(2π.a.{square root}{square root over (μ∈)})

[0127] (f_(c))_(mn) is the cutoff frequency for (m, n) mode.

[0128] At frequencies below cutoff, i.e., evanescent mode waveguideβ_(mn) becomes imaginary given by:

β_(mn) =−jβ.{square root}{square root over ([(f _(c))_(eff) /f] ²−1)}

[0129] A sections of waveguide (circular, rectangular or other types ofcross section) operating below the cutoff frequency can be a utilized asthe inductive portion of the resonator. FIG. 60 depicts the π and Tequivalent circuit for a waveguide below cutoff is provided in George F.Craven, “Waveguide below Cutoff: A New Type of Microwave integratedCircuit”, The Microwave Journal, August 1970, the entirety of which isincorporated herein by reference. This equivalent circuit is simplyderived from regular transmission line equations using imaginarycharacteristic impedance and propagation constant in the evanescentmode. In waveguides operating in evanescent mode, the coupling arms arein effect short antennas have capacitive impedance and furthercapacitances can be provided externally, e.g., external metalization oncircuit board/substrate also are shunt capacitor reactances. FIGS. 61-aand 61-b depict the equivalent circuit for such resonators.

[0130] The techniques discussed in the above section for lumped elementfor finding an equivalent circuit, optimization and fine tuning thedesign applies for the evanescent mode.

[0131] Using Love's equivalence principle, R. E. Collin in chapter 7 ofRobert E. Collin, Field Theory of Guided Waves, 1960, the entirety ofwhich is incorporated herein by reference, derives the relationshipbetween input impedance (Z_(in)=R+jX) of probe or loop coupled into arectangular waveguide and the wave impedance (Z₀). Applying a moregeneral formulation for probe excitation and changing the notationaccordingly, impedance of the probe FIG. %% %%% temp-7.1 is obtained by:

R=2(μ/∈)^(1/2)sin²(β_(mn) l)tan²(βd/2)/(abβ _(mn)β)

X _(mn)=(μ/∈)^(1/2)sin(2β_(mn) l)tan²(βd/2)/(abβ _(mn)β)

[0132] Where R is the radiation resistance due to energy conversion fromelectrical to electromagnetic radiation propagating away from the guideor coupling out through a similar probe. X_(mn) is reactance due to(probe) antennas evanescent fields. The above equations verifies that atfrequencies below cut off the real part of impedance i.e., Z_(in)=R+jXbis zero indicating no dissipative radiation at evanescent mode arepresent in wave guides. However in our structures as depicted in FIGS. 5through 32 there radiations due to the fact that they radiators are opento semi-infinite space and not subject to restricting propagation belowcut-off by the waveguide. Therefore, there is a degradation in the Qfactor of the radiator and shielding provides restricts radiation fromthe coupling arms. FIG. 33 depicts a shielded evanescent mode resonatorin which the above formulation maybe applied. However, the if wideprobes to be used the effect of their capacitances has to be taken intoaccount. capacitance of such conductors

[0133] The capacitive reactance portion of the resonator is obtained bytaking into account the sum of all of the shunt capacitances, i.e., thecapacitance formed on top of the resonator as well as the outside.

[0134] Accurate values for different geometries can be determined by afamily of curves normalized to frequency obtained from electromagneticsimulation. The normalized which normalized to

[0135] 3. Propagating Mode Resonators

[0136] In the case of operating above the waveguide cut-off frequencythe characteristic impedance is a real number given by equation 9-16-ain ref Advanced Engineering Electromagnetics , Constantine A. Balanis,November 1990, the entirety of which is incorporated herein byreference.

Z _(mn)={square root}{square root over (μ/∈)}/{square root}{square rootover (1−(f _(c) /f)²)}

[0137] Each resonator works as a cylindrical wave guide with a short atthe end. This waveguide could operates at frequencies below cut off(Evanescent mode). However, by introducing the reactive components,i.e., the capacitance produced by the micro-strip/strip line a resonanceis established. As the selected relative dielectric constant of thematerial inside the cylinder is increased the resonance frequency getscloser to the cutoff frequency and as a result a wider resonance isobtainable or a smaller diameter would be required for the cylinder. Therequired diameter would be proportional to the inverse of square root ofthe relative dielectric constant.

[0138] Using Love's equivalence principle, R. E. Collin in chapter 7 ofRobert E. Collin, Field Theory of Guided Waves, New York, 1960, theentirety of which is incorporated herein by reference derives therelationship between input impedance (Z_(in)=R+jX) of probe or loopcoupled into a rectangular waveguide and the wave impedance (Z₀).Applying a more general formulation for probe excitation and changingthe notation accordingly, impedance of the probe is obtained by:

R=2(μ/∈)^(1/2)sin²(β_(mn) l)tan²(βd/2)/(abβ _(mn)β)

X _(mn)=(μ/∈)^(1/2)sin2(β_(mn) l)tan²(βd/2)/(abβ _(mn)β)

[0139] Where R is the radiation resistance and X_(mn) is reactance dueto (probe) antennas evanescent fields, β=2π/λ=2π(μ∈)^(1/2) f and λ iswavelength in infinite media, to avoid radiations from propagatingresonators, structures similar to FIG. 33 has to be used.

[0140] Both rectangular and circular or arbitrary cross section such asridged waveguides. A cavity enclosed by metal walls has an infinitenumber of natural frequencies at which resonance will occur. One of themost common types of cavity resonators is a length of transmission line(coaxial or waveguide) short circuited at both ends (The Jordanreference, page30-20). Resonance occurs when

2h=I(λ_(g)/2)

[0141] where,

[0142] I=an integer,

[0143] 2h=Length of resonator,

[0144] λ_(g)=guide wavelength in resonator=λ/[∈_(r)−(λ/λc)²]^(1/2)

[0145] λ=free space wavelength,

[0146] λ_(c)=guide cutoff wavelength

[0147] ∈_(r)=relative dielectric constant of medium in the cavity.

[0148] Where λ_(c) is given by:

λ_(c)=2/[(m/a)²+(n/b)²]^(1/2) for rectangular cavities,

λ_(c)=2πa/χ_(mn) for cylindrical cavities with circular cross section(TM modes),

λ_(c)=2πa/χ′_(mn) for cylindrical cavities with circular cross section(TE modes),

[0149] where χ′_(mn) is the mth root of J′_(n)(χ)=0 and χ_(mn) is themth root of J_(n)(χ)=0 (The Balanis reference pages 472 and 478 providesvalues for χ′_(mn) and χ_(mn)), a is the guide radius.

[0150] 1)

[0151] Excitement of Modes

[0152] In every method of coupling (Micro-strip line, Strip line, slotline and co-planar wave guide) various wave guide modes are exciteddepending on the cutoff frequency of the wave guide evanescent orpropagating modes are excited. However, if the frequency is below thecutoff frequency only evanescent modes are excited. The energycorresponding in each mode is determined by the physical parameters suchas the dimensions and dielectric constants. Due to the complexity ofsuch a problem, electromagnetic simulation using numerical methods(e.g., using commercially available programs such as HFSS™) could beused for an accurate analysis. However, good first order approximationsare obtainable by tight coupling using the techniques of FIG. 12 andassuming the dominant mode of excitement. The dominant mode isdetermined by comparing at the electric field lines in the figurescorresponding to the various modes as FIGS. 9-2 and 8-4 in the Balanisreference respectively for circular and rectangular cross section waveguides.

[0153] Since various modes are excited, the percentage of energycorresponding in each mode is determined by the physical parameters suchas the dimensions and dielectric constants.

[0154] In the case of circular cross section also a combinations ofmodes are excited. For each mode there is a χ′_(mn) or χ_(mn)corresponding to a cutoff frequency of:

(f _(c))_(mn)=χ′_(mn)/2πa{square root}{square root over (μ∈)}

[0155] or

(f _(c))_(mn)=χ_(mn)/2πa{square root}{square root over (μ∈)}

[0156] and depending on the percentages of energy of various modes aneffective cutoff frequency (f_(c))_(eff) would simplify the problem intoa simple waveguide problem, i.e., (f_(c))_(eff) would lead to acalculation of (β_(z))_(eff) from:

(β_(z))_(eff) =β.{square root}{square root over (1−[(f _(c))_(eff) /f]²)}

[0157] where β is 2π/λ and λ is wavelength in infinite media.

[0158] In the case of rectangular cross section also a combinations ofmodes are excited. For each mode there is a χ′_(mn) or χ_(mn)corresponding to a cutoff frequency of:

(f _(c))_(mn)={square root}{square root over((m.π/a)²+(n.π/b)²)}/(2π.a.{square root}{square root over (μ∈)})

[0159] or

(f _(c))_(mn)=χ_(mn)/2πa{square root}{square root over (μ∈)}

[0160] and depending on the percentages of energy of various modes aneffective cutoff frequency (f_(c))_(eff) would simplify the problem intoa simple waveguide problem, i.e., (f_(c))_(eff) would lead to acalculation of (β_(z))_(eff) from:

(β_(z))_(eff) =β.{square root}{square root over (1−[(f _(c))_(eff) /f]²)}

[0161] where β is 2π/λ and λ is wavelength in infinite media. Z is thedirection of propagation which in both cases corresponds to the axis ofthe wave guide which is perpendicular to the cross section.

Z _(t) =Z ₀(Z _(L) +jZ ₀ tan β_(z) l)/(Z ₀ +jZ _(L) tan β_(z) l)

[0162] Where:

[0163] l is the height of the structure,

[0164] Z₀ is characteristic impedance which in this case corresponds towave impedance given by:

Z _(eff)={square root}{square root over (μ/∈)}/{square root}{square rootover (1−[(f _(c))_(eff) /f] ²)}

[0165] and Z_(L)=0 for shorted case and Z_(L)=1/jωc for the case inwhich there is a dielectric layer between the bottom ground and thebottom of the structure and c is the capacitance between the bottom ofthe cylinder and the bottom ground calculated by c=∈A/h.

[0166] Other Types of Cross Section

[0167] Besides the ordinary wave guide cross sections, i.e.,rectangular, circular and eliptical wave guides with more complex crosssections may be used to increase performance with regards to sizereduction. Ridged wave guides accommodate signals in both propagatingand evanescent modes of operations. Due to the extra surfaces that theridges provide the cut-off frequency is lowered and would result asmaller cross section for similar performance in comparison to anordinary shape such as rectangular or circular or elliptical cases. FIG.21 depicts various cross section for ridged guides. Section 8.9 in theBalanis reference discusses the reduction of cutoff frequency as aresult of addition of ridges to a rectangular waveguide. Approximateequation for cutoff frequency of ridged waveguide is given by equation(8-198):

f _(c)={square root}{square root over ((a.b ₀ /a ₀ .b ₀)/[1/(1−a ₀/a)])}/(π.a.{square root}{square root over (μ∈)})

[0168] where a and b are waveguide dimensions and a₀ and b₀ are theridges dimensions. The analysis of this equation as shown in the case ofsingle ridge demonstrates a 5 to 1 decrease in cutoff frequency for.b₀/b=0.1 and a₀/a=0.2 and 6t to 1 decrease in cutoff frequency for.b₀/b=0.1 and a₀/a=0.28. However the ridged waveguides are lossier thanthe ordinary guides and as a result resonators using ridges have lower Qfactors. The cutoff frequencies for various standard single ridgedwaveguides are given in Table-4 page 30-10 of the Jordan reference.

[0169] Using a ridged waveguide lowers cutoff frequency due to increaseof capacitance in the cross section, and as a result β_(z) is increaseand thereby a shorter length of waveguide is required in order to obtainthe same electrical length of β_(z).l.

[0170] Both rectangular and circular or arbitrary cross section such asridged waveguides. A cavity enclosed by metal walls has an infinitenumber of natural frequencies at which resonance will occur. One of themost common types of cavity resonators is a length of transmission line(coaxial or waveguide) short circuited at both ends (The Jordanreference, page30-20). Resonance occurs when

2h=I(λ_(g)/2)

[0171] where,

[0172] I=an integer,

[0173] 2h=Length of resonator,

[0174] λ_(g)=guide wavelength in resonator=λ/[∈_(r)−(λ/λc)²]^(1/2)

[0175] λ=free space wavelength,

[0176] λ_(c)=guide cutoff wavelength

[0177] ∈_(r)=relative dielectric constant of medium in the cavity.

[0178] Where λ_(c) is given by:

λ_(c)=2/[(m/a)²+(n/b)²]^(1/2) for rectangular cavities,

λ_(c)=2πa/χ_(mn) for cylindrical cavities with circular cross section(TM modes),

λ_(c)=2πa/χ′_(mn) for cylindrical cavities with circular cross section(TE modes),

[0179] where χ′_(mn) is the mth root of J′_(n)(χ)=0 and χ_(mn) is themth root of J_(n)(χ)=0 (The Balanis reference pages 472 and 478 providesvalues for χ′_(mn) and χ_(mn)), a is the guide radius.

[0180] Equivalent Circuit

[0181] Each resonator could be modeled as an LC equivalent circuit. Theequivalent circuit can be used for filter design. Calculation of theequivalent circuit is done by one of the following methods:

[0182] 2) Electromagnetic simulation of the structure (usingelectromagnetic simulators such as HFSS™) and comparing the result tomatching the predicted S-parameters to the S-parameters of an LCequivalent circuit.

[0183] 3) Measurement of the structure and comparing the result to matchthe equivalent circuit.

[0184] [

[0185] Tuning

[0186] There are secondary effects such as the interaction betweenremote parts of the resonators. Also the manufacturing tolerancesespecially in case of narrow-band designs play a significant role.Therefore tuning techniques are required. FIG. 40 depicts various tuningtechniques which could be utilized for circuit board type resonators orother types of substrate such as semiconductors. The patches areattached via thin metalization. These patches provide extra capacitanceand are integrated into the layout in provisions to be cut during atuning procedure. The tuning procedure can be performed by a robot thatis fed by a network analyzer measuring parameters of the filter orprobing other parameters. The cuts can be done by laser beam controlledby a robot. Patches provide capacitors and by cutting them of theresonance frequency of the resonator is increased. Also, thew fingers ofinter-digital or inter-spiral capacitors which are used for couplingbetween the resonators or into the resonator can be trimmed inorder tolower the coupling.

[0187] Use of the Resonator in a Filter

[0188] The resonator could be used in structures such as resonatorcoupled fileres described in “electronic Design Handbook” By “Arthur B.Williams and Fred J. Taylor, second edition, Page 5-19 through 5-33.

What is claimed is:
 1. A microwave filter having a resonator comprising:a cylindrical structure having conductive walls filled with a dielectricmaterial, said cylindrical structure recessed inside a multi-layeredsubstrate; a first and second conductive coupling arms disposed on toplayer of said substrate for coupling signals to said cylindricalstructure, said conductive coupling arms being separated by a dielectriclayer, said first and second conductive coupling arms extending awayfrom the center of said cylindrical structure to form a microstrip line;said cylindrical structure further comprising a bottom portion having asolid conductive bottom plate perpendicular to the axis of the cylinder;and a bottom conductive ground layer separated from said conductivebottom plate by a second dielectric layer.